Related papers: 3D-3D Correspondence from Seifert Fibering Operato…
We describe a family of 3d topological B-models whose target spaces are Hilbert schemes of points in $\mathbb{C}^2$. The interfaces separating theories with different numbers of points correspond to braid strands. The Hilbert space of the…
In this paper, we investigate the Seiberg-Witten gauge theory for Seifert fibered spaces. The monopoles over these three-manifolds, for a particular choice of metric and perturbation, are completely described. Gradient flow lines between…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
We introduce a homology theory whose Euler characteristics counts ASD bundles over four dimensional co-associative submanifolds in (almost) G_2 manifolds. As a TQFT, in relative situations, we have the Fukaya-Floer category of Lagrangians…
Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized…
We give a pedagogical introduction to the study of supersymmetric partition functions of 3D $\mathcal{N}{=}2$ supersymmetric Chern-Simons-matter theories (with an $R$-symmetry) on half-BPS closed three-manifolds---including $S^3$, $S^2…
We construct a cohomology theory for oriented links using singular cobordisms and a special type of 2-dimensional Topological Quantum Field Theory (TQFT), categorifying the quantum sl(2) invariant. In particular, we give a description of…
We determine topological properties of Stein domains with boundary diffeomorphic to T^3, S^1\times S^2 and some Seifert fibered 3-manifolds.
In this paper, we study and almost completely classify contact structures on closed 3--manifolds which are totally geodesic for some Riemannian metric. Due to previously known results, this amounts to classifying contact structures on…
An interesting question is whether two 3-manifolds can be distinguished by computing and comparing their collections of finite covers; more precisely, by the profinite completions of their fundamental groups. In this paper, we solve this…
We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres-Douglas theories on $S^1 \times M_3$ with a non-trivial holonomy of a discrete global symmetry along the $S^1$.…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…
We construct an action of 3-cobordisms on the finite dimensional Schr\"odinger representations of the Heisenberg group by Lagrangian correspondences. In addition, we review the construction of the abelian Topological Quantum Field Theory…
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT) and Noncommutative Floer Homology (NCFH). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that…
We introduce regular stratified piecewise linear manifolds to describe lattices and investigate the lattice model approach to topological quantum field theory in all dimensions. We introduce the unitary $n+1$ alterfold TQFT and construct it…
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p=<,> with values in (formal linear combinations of) closed…
In this thesis we study the Seiberg-Witten theory of an oriented homology 3-sphere. The goal is to extract topological invariants - the Seiberg-Witten invariants - by counting the solutions to the Seiberg-Witten equations on the manifold.…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
We introduce in this paper a field theory on symplectic manifolds that are fibered over a real surface with interior marked points and cylindrical ends. We assign to each such object a morphism between certain tensor products of quantum and…